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71.
Lakshman S. Thakur 《海军后勤学研究》1986,33(2):325-358
We implement a solution procedure for general convex separable programs where a series of relatively small piecewise linear programs are solved as opposed to a single large one, and where, based on bound calculations developed in [13] and [14], the ranges of linearization are systematically reduced for successive programs. The procedure inherits ε-convergence to the global optimum in a finite number of steps, but perhaps its most distinct feature is the rigorous way in which ranges containing an optimal solution are reduced from iteration to iteration. This paper describes the procedure, called successive approximation, discusses its convergence, tightness of the bounds, bound-calculation overhead, and its robustness. It presents a computer implementation to demonstrate its effectiveness for general problems and compares it (1) with the more standard separable programming approach and (2) with one of the recent augmented Lagrangian methods [10] included in a comprehensive study of nonlinear programming codes [12]. It seems clear from over 130 cases resulting from 80 distinct problems studied here that significant savings in terms of computational effort can be realized by a judicious use of the procedure, and the ease with which it can be used is appreciably increased by the robustness it shows. Moreover, for most of these problems, the advantage increases as the size, nonlinearity, and the degree of desired accuracy increase. Other important benefits include significantly smaller storage requirements, the ability to estimate the error in the current solution, and to terminate the algorithm as soon as the acceptable level of accuracy has been achieved. Problems requiring up to about 10,000 nonzero elements in their specification and about 45,000 nonzero elements in the generated separable programs resulting from up to 70 original nonlinear variables and 70 nonlinear constraints are included in the computations. 相似文献
72.
In many decision-making situations, each activity that can be undertaken may have associated with it both a fixed and a variable cost. Recently, we have encountered serveral practical problems in which the fixed cost of undertaking an activity depends upon which other activities are also undertaken. To our knowledge, no existing optimization model can accomodate such a fixed cost structure. To do so, we have therefore developed a new model called the interactive fixed charge linear programming problem (IFCLP). In this paper we present and motivate problem (IFCLP), study some of its characteristics, and present a finite branch and bound algorithm for solving it. We also discuss the main properties of this algorithm. 相似文献
73.
74.
作者在前面的文章中报导了扭轮摩擦传动能实现亚纳米级的定位分辨率。然而,这套装置在结构上的复杂之处就是在于采用了静压轴承支撑扭轮。本文指出了扭轮摩擦传动在结构上如何可以简化为采用球轴承支撑扭轮。在简化之后,实验表明定位分辨率小于1纳米。本文得出结论,采用球轴承的扭轮摩擦传动对于在洁净环境下要求实现纳米级定位的制造过程变得更为方便,而且可以取代滚珠丝杠以及常规摩擦传动方式。 相似文献
75.
Properties of a finite-range failure-time distribution, that includes the exponential as a particular case, have been studied. The distribution is IFR when the shape parameter exceeds unity, but is IFRA always. For a given value of the shape parameter, the distribution is NBUE over a segment of its range. Estimators of parameters have been derived. Distributions of two-component series, parallel, and standby system lives have also been worked out. 相似文献
76.
In this article we study the estimation of the average excess life θ in a two-parameter exponential distribution with a known linear relationship between α (the minimum life) and θ of the form α = aθ, where a is known and positive. A comparison of the efficiencies of estimators which are linear combinations of the smallest sample value and the sample sum of deviations from the smallest sample value and the maximum likelihood estimators is made for various sample sizes and different values of a. It is shown that these estimators are dominated in the risk by the minimum-risk scale equivariant estimator based on sufficient statistics. A class of Bayes estimators for inverted gamma priors is constructed and shown to include a minimum-risk scale equivariant estimator in it. All the members of this class can be computed easily. 相似文献
77.
In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view. 相似文献
78.
The present paper extends the results of [7] to cases of multistation lower echelon. For this purpose an algorithm for the optimal allocation of the upper echelon stock among the lower echelon stations is developed. The policy of ordering for the upper echelon is an extension of the Bayes prediction policy developed in [7]. Explicit formulae are presented for the execution of this policy. Several simulation runs are presented and analyzed for the purpose of obtaining information on the behavior of the system, under the above control policy, over short and long periods. 相似文献
79.
Many optimization problems occur in both theory and practice when one has to optimize an objective function while an infinite number of constraints must be satisfied. The aim of this paper in to describe methods of handling such problems numerically in an effective manner. We also indicate a number of applications. 相似文献
80.
A mixed optimization technique for optimal machine replacement is presented which allows much more flexibility than previous models. Optimal purchase, maintenance and sale of a given machine between any two given points in time is treated as a subproblem, which one may choose to solve via control theory, dynamic programming, or practical engineering considerations. (A control theory formulation is used in the paper as an illustration.) These subproblem solutions are then incorporated into a Wagner-Whitin formulation for solution of the full problem. The technique is particularly useful for problems with such asymmetries as an existing initial machine or uneven technological change. A simple numerical example is solved in the Appendix. 相似文献